How to modify the uneven space between separate loop cuts, while they are already cut?
The shipped add-on Loop Tools > Space will space a selection of vertices evenly over the selected range on a single loop. To space the parallel loops in the same move, make the selection on one loop, as shown, and check 'Parallell (all)'. If the points lie on a curve, the tool can make a cubic interpolation to approximate the new positions of the moved points, if you choose.



An edge loop is an end-to-end chain of edges on one side of one, or between two, chains of quad faces. It's what you get when you Alt right-click a single edge in Blender. Alt right-clicking is a good way to test that your mesh is well-formed. If the selection doesn't run where you expect it to, it indicates there is something wrong where the selection stops or diverts; a double vertex, or internal face. (An edge ring is a set of parallel edges along a chain of quad faces - it's what you get when you CtrlAlt right-click a single edge).

In your particular case, you would make a selection of vertices like the ones circled in yellow, all on a single loop. You can probably make that selection more reliably in vertex mode. With 'Selection' set, those vertices would be spaced evenly along their edge. With 'Parallel' set, the vertices on parallel loops (the visible ones circled in red) would also be spaced evenly in their respective ranges. 

If you select vertices on another loop, such as the ones marked in red, the tool will fail - it won't know along which loop you want the vertices to be spaced. Horizontal, or vertical?